All Questions
Tagged with electromagnetism homework-and-exercises
1,550
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Angular velocity of electron in magnetic field
An electron with mass $m$ and charge $-e$ moves in a magnetic field $\mathbf{B}=\nabla \times \mathbf{A}(\mathbf{r})$. It has Lagrangian $$L=\frac{1}{2} m | \dot{\mathbf{r}}|^2-e \,\dot{\mathbf{r}} \...
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A question about Vector Calculus in Electrodynamics
In "Modern Electrodynamics" by Zangwill, on page $91$ equation $(4.3)$ implies that: $$(\vec{r} \cdot \nabla)^n=r_i \ r_j \ r_k \ldots\partial i \ \partial j \ \partial k \ldots \ \ ,$$
...
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Help with local gauge transformation
I have to prove that the following Lagrangian is invariant under local gauge transformation ($\psi\to e^{-i\lambda(x)}\psi$ and $A_\mu\to A_\mu+\partial_\mu\lambda(x)$, where $\lambda$ is real): $$\...
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What's wrong in the concept/method I applied for the below electromagnetism problem?
I was told by mathstack community to post it here.
The setup was this (figure added): a semi infinite wire straight current $I$ being given to a plane sheet (current flows radially there).
Find ...
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What does the "work done" $\frac{dW}{dt}$ in Poynting's theorem mean? Real life examples?
I found an old Related Question here: Can electric and magnetic forces act on their sources?
From the paragraph from Griffith's E&M
Suppose we have some charge and current configuration which, ...
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Computations with Tensors
I have the following ansatz
$$T^{\mu\nu}=AF^{\mu\alpha}F_{\alpha}^\nu+B\eta^{\mu\nu}F^{\alpha\beta}F_{\alpha\beta}$$
for some constants $A,B.$ Here, $F_{\mu\nu}$ is the electromagnetic field tensor, ...
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Why can’t we write $\overrightarrow{\nabla} \cdot \overrightarrow{M} = \chi_m \overrightarrow{\nabla} \cdot\overrightarrow{H}$?
We know that $\overrightarrow{B} = \mu_0 (\overrightarrow{H} + \overrightarrow{M})$.
$\therefore \overrightarrow{\nabla} \cdot\overrightarrow{B} = \mu_0 (\overrightarrow{\nabla} \cdot\overrightarrow{H}...
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Classical Harmonic Oscillator in a Magnetic Field
Consider a 3D charged Harmonic Oscillator which is placed in a homogenous magnetic field along the z direction. The equations of motion in plane are then given as:
$$
m\ddot{x}=kx+a\dot{y},$$
$$
m\...
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A difficulty in understanding "Kinetic Momentum" of A Charged Particle in a Magnetic Field
Maybe the title is not accurately stated.
There are few doubts about my question itself, these are-
Is Kinetic Momentum an operator?
I said "A Charged Particle", not "A Moving Charged ...
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Magnetic Potential and Magnetic Field of a Permanent Cylindrical Magnet
The magnet has magnetization $\vec{M}=M_0 \hat{k}$, radius $r=b$, and length $L=2l$, we need to find the potential $A$ along its $z$ axis and then the magnetic field $\vec{B}$. The equation where one ...
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What happens if a charged capacitor is connected to the ground on both sides through resistors? [closed]
Imagine we have the circuit below:
When the switch is connected to (a), we will be charging the capacitor. After the capacitor is fully charged, the left side of capacitor will be at 5V and right ...
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How to connect $x$, $y$ component of 2D electromagnetic wave equation?
I want to solve following Maxwell's equation.
$$
\triangledown ^{2}E+\frac{\omega^{2}}{c^{2}}E=0
$$
But, Electric field has x, y component in 2D geometry.
So, it will be
$$
\frac{\partial^{2} E_x}{\...
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How is $E×B$ zero? [closed]
I was reading Feynman lectures vol. 2 pg no. 291. There I found the general solution of one dimensional planar waves along $x$ direction. My question is the when I apply dot product on $E$ and $B$ ...
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What causes Magnetism and Why Copper is not attracted by a Magnet?
I don't know much about electromagnetism and magnetism, but I do understand some things. Recently, a question has been going around my head, so I did some research of my own, and now I'm confused and ...
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Charge in crossed $E$ and $B$ fields
This post describes the motion of a charge in crossed electric and magnetic fields as:
$$
x = r \cos ωt + \dfrac EB t\\
y = r \sin ωt\\
$$
Can you please explain how these equations are derived. Why ...
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Magnetic dipole moment due to folded loop [closed]
A steady current i flows in a small square loop of wire of side L in a horizontal plane. The loop is now folded about its middle such that half of it lies in a vertical plane. Let
$
μ_1
$
and
$
μ_2
$
...
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Equations of motion of $\mathcal{L}= - \frac{1}{4}F^{2}_{\mu \nu} - A_{\mu}J_{\mu}$ in momentum space
I'm reading the Matthew D. Schwartz, Quantum field theory and the standard model, p.128 and some question arises.
Consider a lagrangian $\mathcal{L}= - \frac{1}{4}F^{2}_{\mu \nu} - A_{\mu}J_{\mu}$ ($...
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My doubt is regarding the lorentz force
Consider a magnetic field in the positive z direction, and a charge +q moves with a velocity along the positive x direction. How do we know in which direction lorentz force on charge will be acting?
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Lorentz force from potential- extra term?
I'm trying to verify the E.M potential energy $U= \int{A_\mu J^\mu} = q(\phi - A_j v^j )$ by using the connection:
$$
F= - \frac{\partial U}{\partial r} + \frac{d}{dt} \frac{\partial U}{\partial v}
$$...
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Unpolarized light incidence
A beam of unpolarized light carries 2000W/m2 down onto an air–plastic interface. It is found that of the light reflected at the interface 300W/m2 is polarized with its $E$-field perpendicular to the ...
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680
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Application of Biot-Savart's law on a current-carrying wire of finite length
In this figure, how will the wire elements between O&a and O&-a affect the magnetic field at point 'P' which lies at a distance x from point O? Because none of the field lines created due to ...
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How to find current density given resistor, and voltage, using Ohm's law in this case?
I was wondering about how to find current density, given a resistor and an electromotive force.
resistor's data are: resistivity = $\rho$, length = $l$, and cross sectional area = $A$.
resistor = $\...
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Beginner electricity and magnetism problem
The answer is: "Excess electrons will flow onto the ball's left edge only, causing a repulsive force to push the ball to the right."
Does the "ball's left edge" refer to only the ...
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300
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How is current produced by one rotating charged sphere? [closed]
I was doing this problem today:
This question came in the Dhaka University admission exam 20-21
Q) A sphere with charge $q$ is rotating by a non-conducting string at an angular speed $\omega$. What is ...
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Why is induced electric current moving clockwise/counterclockwise?
I know that if I want to identify north pole and south pole of a magnet I can create an electric circuit using a battery (an EMF) and a copper wire. I create a solenoid of N turns, and move a magnet ...
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Relation between Area under $I$-$H$ hysteresis Loop and $B$-$H$ hysteresis Loop [closed]
If the area under the I-H hysteresis loop and B-H hysteresis loop are denoted by $A_1$and $A_2$ (The symbols have usual meaning as set in electromagnetics), then
$A_2=\mu_oA_1$
$A_2=A_1$
$A_1=\...
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340
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How much can we push the plates of capacitor?
I am currently a highschooler and came across this question in physics
A capacitor of plate area $A$ and separation $d$ is connected to battery of emf $V$ and is charged to steady state. Now the ...
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56
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Mass Spectrometer [closed]
Say, we have a mass spectrometer and we want to determine the mass ratio of Hydrogen and Deuterium. Suppose the ions are positively charged and $q=1.6 \times 10^{-19}C$. The magnetic field can be set ...
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How to identify north pole of a magnet using only a battery, and a copper wire? [closed]
I have a magnet, a copper wire, and a battery. I need to find the north pole, and the south pole of a magnet using only these items. (not a compass).
Here's my attempt: create a circuit, battery is ...
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Which configuration is better for this electric motor?
I have a problem with this exercise, it's an electric motor.
an electric motor works because of a magnet, and a wire with a current (i.e electrons moving in it). by turning on and off the current it's ...